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Proof step 8 from proof indices-set-erasing (previous step)

wlar[m0] = wl-entry(m1, erasing), wlar[m, wl-entry(n, erasing)][m0] = wl-entry(m2, stat), m0 < # wlar, indices-erasing(wlar, nx0), ∀ wlar, m, n. indices-erasing(wlar, nx0) → indices-erasing(wlar[m, wl-entry(n, erasing)], nx0) ⊦ stat = erasing ∧ indices-erasing(wlar[m, wl-entry(n, erasing)], nx0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ m ≠ n → wlar[n, wle][m] = wlar[m]
Proof step 10:
wlar[m, wl-entry(n, erasing)][m0] = wl-entry(m2, stat), wlar[m0] = wl-entry(m1, erasing), m0 = m, m0 < # wlar, indices-erasing(wlar, nx0), ∀ wlar, m, n. indices-erasing(wlar, nx0) → indices-erasing(wlar[m, wl-entry(n, erasing)], nx0) ⊦ stat = erasing ∧ indices-erasing(wlar[m, wl-entry(n, erasing)], nx0)
Proof step 14:
wlar[m0] = wl-entry(m2, stat), wlar[m0] = wl-entry(m1, erasing), m0 < # wlar, indices-erasing(wlar, nx0), ∀ wlar, m, n. indices-erasing(wlar, nx0) → indices-erasing(wlar[m, wl-entry(n, erasing)], nx0) ⊦ m0 = m, stat = erasing ∧ indices-erasing(wlar[m, wl-entry(n, erasing)], nx0)

Rule argument

spec: array, inst: wlarray-base name: Put-other seq: ⊦ m ≠ n → wlar[n, wle][m] = wlar[m] subst: [m, wle, n, wlar] → [m0, wl-entry(n, erasing), m, wlar] flags: <all paths>

Additional information

Used terms: m0, wl-entry(n, erasing), m, wlar